Cryptology ePrint Archive: Report 2010/121

Abstract: We propose a simple and efficient construction of CCA- secure
public-key encryption scheme based on lattice. Our construction
needs an encryption scheme, which we call \matrix encryption", as building block, and requires the underlying matrix encryption scheme to satisfy only a relatively weak notion of security which can be achievable without random oracles. With the pseudohomomorphism property of mR04 of [3], which is the multi-bit version of single-bit cryptosystems R04 [1], we design a matrix encryption scheme which satisfies the above requirements, thus, our construction provides a new approach for constructing CCA-secure encryption schemes in the standard model. So far as we know, our construction is the first CCA-secure cryptosystem which is directly constructed from lattice and whose security is based on the unique shortest vector problem (uSVP).
In addition, the method designing the matrix encryption scheme from
mR04 also adapts to mR05, mA05, mADGGH of [3], which are the multibit
versions of single-bit cryptosystems R05 [2], A05 [5], and ADGGH [7],
respectively, since they have the same pseudohomomorphism property as
mR04. This result makes our approach constructing CCA-secure cryptosystem become generic and universal.